$J$ $K$ $L$ If: $ KL = 2x + 2$, $ JL = 55$, and $ JK = 7x + 8$, Find $KL$.
Answer: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {7x + 8} + {2x + 2} = {55}$ Combine like terms: $ 9x + 10 = {55}$ Subtract $10$ from both sides: $ 9x = 45$ Divide both sides by $9$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $KL$ $ KL = 2({5}) + 2$ Simplify: $ {KL = 10 + 2}$ Simplify to find ${KL}$ : $ {KL = 12}$